So...the problem... (E denotes epsilon, D delta)

For anyone that may need a reminder...what we're trying to show is the limit of f(z) = w0 as z->z0 by demonstrating that for any E>0 there exists a positive D such that:

|f(z) - w0| < E whenver 0 < |z-z0| < D.

The limit i'm trying to prove: limit of 1/z = i as z->-i.

So that gives me: |1/z - i| < E whenever |z+i|<D.

Then I know I need to try and get the |1/z-i| in terms of |z+i|...but that's where my hang-up is.

Through some manipulations...I've gotten that |1/z-i| = |z+i|/|z|...but there's still that annoying z term.

If I change it to |z+i|/|z+i-i|, I can do the triangle inequality in reverse and get:

|z+i|/|z+i-i| <= |z+i|/(|z+i|-1).

And there...I'm stuck. Trying to say D=E/k and substitute that into the above doesn't work out too good. Dividing top/bottom by |z+i| gets me something in the form of 1/1-x...but the power-expansion doesn't converge >.<

So with that, I've just about run out of ideas... Do I even have the right approach?? I don't want the whole proof...just a hint.

Thanks,

-Eric